TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 8, August 201
4, pp. 5954 ~ 5962
DOI: 10.115
9
1
/telkomni
ka.
v
12i8.563
4
5954
Re
cei
v
ed
Jan
uary 15, 201
4
;
Revi
sed Ma
rch 3, 2
014;
Acce
pted Ma
rch 1
6
, 2014
Electric Field and Thermal Properties of Wet Cable:
Using FEM
Sushman Ku
mar Kanikell
a
Dept of Electric
al an
d Electro
n
i
cs Engg, NIT
K
, Surathkal, Ma
nga
lore, Kar
n
a
t
aka, India
E-mail: sushm
an2
54@
gmai
l.com
A
b
st
r
a
ct
A Sing
le p
has
e medi
u
m
vo
ltage
pow
er ca
ble (X
LPE) bu
ried i
n
so
il a
n
d
it can
be u
s
ed t
o
investi
gate el
e
c
tric field, pote
n
tial
distri
buti
o
n and incr
eas
e
d
temp
eratur
e
of the cable i
n
sulati
on w
i
th rising
loa
d
currents, are know
n to a
cceler
a
te the formatio
n
of
w
a
ter and el
ectric
trees in cabl
e
s
w
h
ich ultimately
lea
d
to cab
l
es
failur
e
. T
o
determine th
e the
r
ma
l an
d el
ectrical b
e
h
a
vior
o
f
a given w
e
t cabl
e insta
llati
o
n
.
T
he w
o
rk presented i
n
this p
aper i
n
volv
es the use
of CO
MSOL multi
p
h
ysics F
i
nite El
ement softw
are to
deve
l
op an int
egrate
d
el
ectri
c
al,
ther
ma
l mode
l
w
i
th
3
mi
cro meter w
a
te
r bub
ble r
adi
us
. T
he prese
n
c
e
of
w
a
ter tree resu
lts in the red
u
c
t
ion of their d
i
e
l
ectric
strength.
Here the F
i
n
i
te Ele
m
e
n
t simulati
on tech
niq
u
e
is used to
11k
V and
20kV p
o
w
e
r cabl
es. A mo
del th
at ill
u
s
trates the w
a
ter-die
lectric i
n
terface w
i
thin t
h
e
cable insulation syst
em
is pr
oposed.
Ke
y
w
ords
:
po
w
e
r cable, F
E
M, comsol
mu
ltiph
ysics, e
l
ectri
c
field an
d temperatur
e
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Electri
c
power system reliability start fr
om generat
ing, transmission
comes
up with
distrib
u
tion. A
t
pre
s
ent, the
power
ca
ble
acts
as
the
key role i
n
po
wer tran
smi
s
sion. T
o
op
erate
cabl
e net
works fo
r p
o
wer
transmissio
n
kno
w
le
dge i
s
need
ed of th
e maximum
current loa
d
th
at
can b
e
appli
ed witho
u
t damage
re
sult
ing to the
ca
ble. Und
e
rg
round
con
s
tru
c
tion could b
e
a
rea
s
on
able
al
ternative to o
v
erhea
d in u
r
ban a
r
ea
s, where
an ove
r
head lin
e can
not be in
stall
e
d
with app
ro
pri
a
te cle
a
ra
nce, at any co
st. In s
uburba
n are
a
s, a
e
st
hetic i
s
sue
s
, weath
e
r-rel
a
ted
outage
s, so
me environm
ental con
c
erns, an
d the
high
co
st of some
ROWs coul
d ma
ke
an
unde
rg
roun
d
option mo
re a
ttractive. The
s
e con
s
tru
c
ti
on limitations
often increa
se the co
st of the
proje
c
t [1].
The tren
chin
g for th
e constructio
n
o
f
unde
rgroun
d line
s
cau
s
es
gre
a
ter
soil
disturban
ce t
han ove
r
he
a
d
lines. Ove
r
head lin
e co
n
s
tr
u
c
tion di
st
urb
s
the soil
mostly at the
site
of each tra
n
smissi
on pol
e. The pre
s
e
n
ce
of water withi
n
the insulati
on material
s
can only lea
d
to
forming
wate
r trees if a
sufficient ele
c
tri
c
field
exists. T
herefo
r
e, ma
ny works hav
e indicated th
at
the initiation of water tre
e
depe
nd
s on the magnitu
de
of electri
c
tre
e
s an
d wate
r availability [2].
In the present
wo
rk, a
mod
e
l for m
edium
voltage p
o
wer
cabl
e is de
scribe
d b
a
se
d on th
e
FE techni
que
. This mo
del
comp
ri
se
s region
s of in
sulation mate
rial and
wate
r particl
es
wit
h
elliptical ge
o
m
etric
stru
ctu
r
e for field an
d therma
l mo
del. The field enha
ncement
as a function
of
sha
r
pn
ess of
water pa
rticl
e
s is dete
r
mi
ned. The
pot
ential and fiel
d stren
g
th values throug
h
out
the insulatio
n
are
cal
c
ul
ated for
cabl
e und
er
wet
con
d
ition. T
he thermal
model
com
p
rise
s
temperature
distrib
u
tion throu
gho
ut the cable
st
ru
cture. Th
e si
gnifica
nce of the simulation
techni
que
s in comp
ari
s
o
n
with the actual expe
ri
mental meth
ods is hi
ghli
ghted. Finall
y
, the
results a
r
e
u
s
ed to
demo
n
strate t
he
mech
ani
sm
s
respon
sibl
e for tre
e
initiat
i
on an
d gro
w
th,
whi
c
h could b
e
develop
ed to cau
s
e b
r
ea
kdo
w
n in
side
the cabl
e insulation.
2
.
Rese
arch method
2.1. Comsol Multiph
y
sics Soft
w
a
r
e
Two
-
dime
nsi
onal
CO
MSO
L
M
U
LTIPHY
SICS so
ft
ware was u
s
e
d
i
n
the
present
study.
This Softwa
r
e p
r
ovide
s
a
u
tomatic me
sh
gen
eratio
n for solving
ele
c
tro
s
tatic,
ele
c
trom
agn
etic
and
Heat tra
n
sfer proble
m
s by a
differential o
p
e
r
at
or FE meth
o
d
. The
comp
utational p
r
op
ertie
s
of the COMS
OL are
enabl
ed.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Electri
c
Field
and The
r
m
a
l Prope
rties of
Wet Ca
ble: Using FEM (S
u
s
hm
an Kum
a
r Kanikella)
5955
a) field and p
o
tential value
s
at any boun
dary to be plo
tted,
b) the display
of equipotent
ial and field lines in me
sh
e
d
regio
n
s.
Detaile
d de
scriptio
n of F
E
formulatio
n
prin
cipl
es
a
nd p
r
o
c
ed
ure
s
can
be fo
u
n
d in th
e
use
r
ma
nual
of su
ch a
pa
ckage i
s
avai
lable in
pap
e
r
[3] .In our
ca
se two mo
dule
s
are u
s
ed
those
are
ele
c
tro
s
tatic a
n
d
heat tran
sfe
r
module
be
ca
use
ele
c
tro
s
tatic mod
u
le
consi
s
t of ele
c
t
r
ic
field and pot
ential model
s and heat transfe
r mod
u
l
e
con
s
i
s
t of temperature
distrib
u
tion in
a
cabl
e.
Figure 1. Flow Ch
art for COMSOL Multi
physi
cs for
O
b
taining Solut
i
on
2.2. Sy
stem
Con
f
igura
tion
In ord
e
r to
st
udy the el
ectric field, p
o
ten
t
ial and tem
p
eratu
r
e di
stri
bution
cha
r
a
c
teristics
in cabl
e insu
lation, the Comsol M
u
ltip
hysics
FE co
mputer
software i
s
used to build a two-
dimen
s
ion
a
l
model fo
r the
cabl
es
und
er
study a
s
the
i
n
vestigate
d
field line
s
are
perp
endi
cul
a
r to
equip
o
tential
lines a
nd di
re
cted fro
m
co
n
ducto
r to
the
outer
she
a
th
of the cabl
e, a se
ction m
a
de
across th
e
cable
ca
n illu
strate
the
circumfe
ren
c
e
and
sh
arp
e
dge
s of th
e
ellipsoids ali
gned
along the
s
e fi
eld line
s
[4].
Table 1. Ca
bl
e Paramete
rs
Voltage(kv)
Conductor R
adiu
s
(mm)
Insulation thickn
ess(mm)
11
3.9088
5.897
20
2.4333
1.456
The investigation of field development at t
he ellipse sides and the
determi
nation of its
enha
ncement
at the sha
r
p
end
s of the el
lipsoi
d
s a
r
e
a
c
hieve
d
by in
spe
c
ting th
e field dist
ributio
n
on the plane of cable se
ction. The lateral com
ponent of electri
c
field around the ellipsoi
d
surfa
c
e,
whi
c
h pen
etrate
s
the ca
ble d
e
p
th ha
s le
ss
value than th
at at the ho
ri
zontal
ellip
soi
d
edge
s.
The cable configu
r
ations
used i
n
the thre
e case
studi
es a
r
e tabul
ated i
n
Table
1 sh
own
above [4]. Each µcable co
mpri
se
s of an inner
Cop
p
e
r co
ndu
cto
r
and oute
r insulation of pa
per
whi
c
h h
a
s
a
permittivity of 3.6. It has
b
een
rep
o
rted
that the am
ount of
water,
which can be
absorb
e
d
by
cabl
e in
sul
a
tion, vari
es in
the
ran
ge
2-6
%
of the
total
insulation
vo
lume [5], a
n
d
in
the pre
s
ent
analysi
s
, the abso
r
ption
wa
s taken to
be 3%. The radiu
s
of the sphe
ri
cal water
dropl
et varie
s
in the range
of 0.1 to 5µm [6]. It is taken
here to be 3
µ
m.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 595
4 –
5962
5956
Figure 2. Pro
posed Mod
e
l of Water
Con
t
ent in
the Single Ph
ase Po
we
r Cable
Figure 3. Pro
posed Mod
e
l of Water
Con
t
ent in
the Single Ph
ase Po
we
r Cable
The
computation
o
f
elect
r
ic
field
di
st
ribution,
it is a
r
rogate
d
that th
e
wa
ter b
ubble
s
a
r
e
distrib
u
ted
ra
dially along t
he line
s
em
a
nating fro
m
the condu
cto
r
surfa
c
e to
th
e
outer
surf
ace of
insul
a
tion, a
s
dem
on
strate
d in
Figu
re
2
.
If it is a
r
rog
a
ted that t
h
e
elon
gation
o
f
wate
r void
to
form an
ellipse does not alt
e
r it
s area, the numb
er of water
voids per r
adi
al line
can be
ciphered
as in
dicated i
n
Tabl
e 3. Th
ese
num
bers
also
sati
sfy the co
ndition th
at bubbl
es
ad
jace
nt to cabl
e
conductor
and subsequent
bubbles
in the insulation will not over
lap. Figure 3
depicts how these
bubbl
es a
r
e
arrang
ed to form sectio
ns of cable
in
sulation re
stri
cted betwe
en
pairs of ro
ws of
water voi
d
s.
On the other h
and, the ele
c
tro
s
ta
tic field anal
ysis is
simp
lified usin
g thi
s
symmetri
c
al
model in which the total number of no
de
s and the tria
ngula
r
eleme
n
ts.
Table 2. Water Void Configuration
Voltage(kV)
Bubble Radius(µm)
Water
Voids
Voids/radial line
Elements genera
t
ed
11
5µm
145275
23
3495
20
5µm
230021
38
6212
To facilitate computation
of electri
c
field
distri
buti
on, it is as
sumed that the water
bubbl
es
are distrib
u
ted ra
dially
alon
g t
he lin
es ema
nating from t
he
con
d
u
c
tor su
rfa
c
e to
the
outer surfa
c
e
of in
sulatio
n
, as de
mon
s
trated in
Fi
g
u
re 2. If it i
s
a
s
sume
d th
at the el
ong
ation
of
water pa
rticle
to form
an el
lipse
doe
s
no
t alter its
are
a
, the nu
mbe
r
of
water bu
bble
s
pe
r
rad
i
al
line,
P
N
can b
e
calculated from Equation
(1). Equ
a
ti
on
(2) give
s the
area of ellip
se, whi
c
h i
s
assume
d to be equivalent t
o
a circula
r
area of water b
ubble.
wp
2
2
2
P
r
)
r
R
(
DM
5
.
0
N
(
1
)
Area of ellipse =
π
ab
(2)
Whe
r
e R
i
s
th
e oute
r
radi
u
s
of th
e
cabl
e
;
r
i
s
the
ra
diu
s
of th
e
con
d
u
ctor;
M
i
s
th
e pe
rcentag
e
of
absorb
ed wat
e
r;
wp
r
the ra
diu
s
of the wate
r p
a
rticle;
a
and
b
are th
e maj
o
r an
d mino
r
axes of the
elliptical
sha
ped water pa
rticle. The p
a
r
amete
r
D
i
s
repo
rted a
s
a prop
ortio
n
a
l
value, relating
that part of the circle restri
cted bet
wee
n
two
adja
c
ent
radial line
s
to the whol
e ci
rcle
Acco
rdi
ng to
the qu
oted v
a
lue
s
of
co
nd
uctor
radiu
s
and i
n
sulatio
n
thickn
ess
a
bove, the
numbe
r of
water b
ubble
s
in ea
ch lin
e i
s
vari
ed. Thi
s
nu
mbe
r
al
so sati
sfies th
e co
ndition t
hat
bubbl
es a
d
ja
cent to ca
ble
con
d
u
c
tor an
d sub
s
e
que
nt bubble
s
in th
e insul
a
tion will not overlap
.
The diffe
ren
c
e in th
e dim
e
nsio
ns of the
wate
r b
ubbl
es
and
the
surroun
ding
di
electri
c
,
contai
ning th
ese
bub
ble
s
, is si
gnificant
. This mi
sma
t
ch in dim
e
n
s
ion
s
a
c
tuall
y
leads to
so
me
inco
nvenien
ce in the illu
stration of the
studied
mo
del and i
n
the selectio
n
of the accu
rate
sub
d
ivision
s
durin
g me
shi
ng process o
f
various
re
gi
ons
of the m
odel. The
Fig
u
re 4
sh
ows
all
water b
ubbl
e
s
along
with the radi
al line and individu
al
elliptical wat
e
r bub
ble sha
pe co
nsi
s
ting
of
minor a
nd ma
jor axis.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Electri
c
Field
and The
r
m
a
l Prope
rties of
Wet Ca
ble: Using FEM (S
u
s
hm
an Kum
a
r Kanikella)
5957
Figure 4. Elliptical Shape of
Water Bub
b
l
e
Figure 5. Co
mputational S
egment for F
E
Simulation
3. Results a
nd Discu
ssi
on
Whe
n
the i
n
sulation
syste
m
is free
of
water, th
e p
o
t
ential and
field value
s
ha
ve been
decrea
s
in
g in
unequ
al ste
p
s from the
con
d
u
c
tor
su
rface to the
cabl
e out
er sheath.
Ho
we
ver,
whe
n
the water pa
rticl
e
s a
r
e incl
uded
wit
h
in the in
sula
tion are
a
, the
field and e
q
u
i
potential line
s
sho
w
m
o
re d
i
vergen
ce
co
mpared
with
the dry
ca
se.
This no
n u
n
i
f
orm di
strib
u
tion of fiel
d a
n
d
equip
o
tential
lines b
e
come
s mo
re noti
c
e
able at the
di
electri
c
-water interfac
e, as the permittivity
of the water i
s
sig
n
ifica
n
tly greate
r
than
the diele
c
tric.
Whe
n
the
wa
ter voids
are
sne
a
ked in th
e ca
ble in
sul
a
tion, the ele
c
tri
c
field at the tips
of
elliptically sh
aped
wate
r p
a
rticle
s
will b
e
much hig
h
e
r
. With a
relat
i
ve permittivity of water
r
E
=80
[6] comp
ared
with the
cabl
e
insulation permittivity (
r
E
=3
.6) it is expe
cted to find th
at the field i
s
heavily disto
r
ted in the vici
nity of
water
bubbl
e. To in
vestigate the
influen
ce of the ele
c
tri
c
field
distrib
u
tion o
n
the wet in
sulation of the
cable, it wa
s nece
s
sa
ry to con
c
ent
rate
on one
elliptical
sha
pe
of water p
a
rti
c
le
s.
The m
agnitu
de of th
e
el
e
c
tri
c
field
wa
s
cal
c
ulate
d
for a
num
ber of
points lo
cate
d in the symmetrical se
ction. T
here a
r
e several factors which wi
ll determine t
he
thermal
beh
a
v
ior of a give
n ca
ble in
stal
lation.
The
s
e
inclu
de the
assume
d am
pacity, the ca
ble
con
s
tru
c
tion
and ci
rcumst
ances of inst
allation, t
he therm
a
l pro
p
e
r
ties of the su
rro
undi
ng soil
and
the ambient tempe
r
ature. The pri
n
ci
pal heat so
urce i
n
the probl
e
m
is the Joul
e heat dissip
ated
in the con
d
u
c
tor(s). The transfe
r of this heat
to the surroun
ding
s i
s
gove
r
ned b
y
the geomet
ry
and mate
rial
prop
ertie
s
of the con
d
u
ctor, in
su
l
a
tion, scre
enin
g
, she
a
thing
and tre
n
ch
fill
material
s a
s
well a
s
the a
m
bient condit
i
ons a
r
e
sho
w
n in Fig
u
re 6. The therm
a
l and el
ectri
c
al
system
s a
r
e
cou
p
led via t
he temp
eratu
r
e d
epe
nden
ce
of th
e resi
stivities of th
e co
ndu
cto
r
an
d
s
h
eath materials
[7].
Figure 6. Field and Tem
p
e
r
ature Di
strib
u
tion in
Wet
Cabl
e for 11
kV Water Bub
b
le Ra
diu
s
5µm
In the normal
operatio
n of
a cable, the
heat lo
ss, if any, is disreg
arde
d. Ho
we
ver, the
thermal
in
sta
b
ility, being
a
co
nsequ
en
ce of mi
sm
atch
bet
wee
n
st
eady state he
at
develo
ped
and
dissipate
d
, appea
rs to
be
sen
s
itive to o
m
issi
on of
h
e
a
t input functi
on. The
comp
lexity arising
out
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 595
4 –
5962
5958
of the in
clu
s
i
on of thi
s
add
itional term i
s
, admittedly,
con
s
id
era
b
le.
Ho
weve
r, in
orde
r to
be
a
b
le
to comp
ute the tempe
r
atu
r
e di
strib
u
tion
to a
high
er
degree of a
c
curacy, it be
comes
ne
ce
ssary
to take into a
c
count the he
at input func
ti
on de
spite m
a
thematical complexity [10].
3.1. General
Discus
s
ion
The Elect
r
ic fi
eld and the
r
m
a
l prop
ertie
s
of wet cabl
e is plotted he
re
for two ca
se
s they
Are:
a)
11kV op
erating voltage, 5 micro
meter
Radi
us of water bub
ble.
b)
20kV op
erating voltage, 5 micro
meter
Radi
us of water bub
ble.
The plots a
r
e
plotted for ea
ch case co
nsi
derin
g:
a)
Electri
c
field,
potential a
nd
temperatur
e
distrib
u
tion al
ong the
Cu
rv
e line
con
n
e
c
ting
numbe
r of wa
ter bubbl
es.
b)
Electri
c
field, potential an
d temperatur
e
distrib
u
tion in
side the
wate
r bubbl
e cu
rv
e.
c)
Electri
c
field, potential an
d temperatur
e
distrib
u
tion al
ong the Radi
al line of wate
r
bubbl
e
3.2. Electric
Field, Potential and
Temper
a
t
ure
Distribu
tio
n
along th
e Curv
e Line
Conn
ecting
Number o
f
Wa
ter Bubbl
es
Potential (kV
)
Figure 7.a.Electri
c
Potenti
a
l Distri
bution
along the
Curve Conn
ectin
g
Numb
er of
Wate
r
Bubble
s
11
kV
Figure 7.b. Electri
c
Potenti
a
l Distri
bution
along the
Curve Conn
ectin
g
Numb
er of
Wate
r
Bubble
s
20 kV
Field (kV/m)
Figure 8.a. Electri
c
Field
Di
stributio
n alo
ng the
C
u
r
v
e
C
o
nn
ec
tin
g
Nu
mb
er o
f
W
a
te
r
Bu
bb
le
s
11kV
Figure 8.b. Electri
c
Field
Di
stributio
n alo
ng
the Curve Li
n
e
Con
n
e
c
ting
Numbe
r
of Wate
r
Bubble
s
20
kV
2.
8
2
2
2
.
822
5
2.
823
2.
8235
2.
824
2.
8245
2.
825
2
.
825
5
2.
826
2.
8265
2.
827
9
980
9
985
9
990
9
995
10
000
Ho
r
i
zo
n
t
a
l
d
i
s
t
a
n
ce(m
m
)
P
o
te
n
tia
l(
V
)
4
.
649
4.
6
495
4.
65
4.
65
05
4.
65
1
4.
65
15
4.
65
2
4.
65
25
4.
65
3
4.
65
35
4.
65
4
8
860
8
870
8
880
8
890
8
900
8
910
H
o
r
i
z
o
n
t
al
d
i
s
t
an
c
e
(
m
m
)
P
o
t
e
n
t
ia
l(
V
)
4.649
4.6495
4.65
4
.
6505
4.651
4.6515
4.652
4.6525
4.653
4.653
5
4.654
2.8
3
3.2
3.4
3.6
3.8
4
x 10
7
H
o
r
i
z
o
nt
a
l
di
s
t
a
n
c
e
(
mm
)
E
l
et
cri
c f
i
e
l
d
(
V
/
m
)
4.
6
4
9
4.6
495
4.6
5
4.
650
5
4.
651
4
.
65
15
4.6
5
2
4
.
65
25
4.
6
5
3
4.6
5
3
5
4.
6
5
4
2.
8
3
3.
2
3.
4
3.
6
3.
8
4
x 10
7
Hor
i
z
on
tal
d
i
s
t
a
n
c
e
(
mm
)
E
l
et
cri
c f
i
e
l
d
(
V
/
m
)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Electri
c
Field
and The
r
m
a
l Prope
rties of
Wet Ca
ble: Using FEM (S
u
s
hm
an Kum
a
r Kanikella)
5959
Figure 7.a,
7.b and
8.a
8.b illustrate the va
lue
s
of ele
c
tri
c
field, poten
tial and
temperature
along the
radi
al line conn
ecting a num
ber of water
bub
bles. Th
e ra
di
ally lined wate
r
voids comput
ed along the
line con
n
e
c
ting the wate
r bubbl
es for 1
1
kV and 2
0
kV, 5
μ
m vo
lta
ge
rating
s for
ca
se 1. By ob
serving the
s
e
plots t
he field
is maximum
at con
d
u
c
tor
surfa
c
e
and t
hen
decrea
s
e
s
to
wards
water
bubbl
e a
nd t
he pl
ots are
plotted
with
resp
ect to
h
o
rizontal
di
stan
ce
from
con
d
u
c
tor to
the
sh
eath. Be
cau
s
e the
ele
c
tri
c
field va
rie
s
with
re
spe
c
t
to dista
n
ce i.
e.
electri
c
field is inversely proportio
nal to the dist
an
ce [
22] similarly for potential a
nd temperatu
r
e,
in plot base-a
indicate
s 11
kV and base -b indicates 2
0
kV.
Tempera
t
ure
(K)
Figure 9.a. Tempe
r
ature Distributio
n alo
ng
Curve
Con
n
e
c
ting Numbe
r
of Water
Bubble
s
11
kV
Figure 9.b. Tempe
r
ature
Distributio
n alo
ng the
Curve
Con
n
e
c
ting Numbe
r
of Water
Bubble
s
20
kV
The
temp
erature distri
butio
n
from co
ndu
ctor su
rfa
c
e t
o
the
radial
li
ne conn
ectin
g
wate
r
bubbl
e is illu
strated in Figu
re 9.a and
9.b. The temp
e
r
ature at the vicinity of the water p
a
rticl
e
s
is g
r
e
a
tly intensifie
d
com
pare
d
with t
hat at
t
h
e sa
me
lo
cat
i
o
n
whe
n
th
e wate
r
pa
r
t
ic
le
s
a
r
e
absent.
Th
e maximum bo
unda
ry condi
tion
of
tem
p
eratu
r
e
at co
ndu
ctor surfa
c
e i
s
363K
a
nd
outer sheath t
e
mpe
r
ature is 293K.
3.3. Electric Field, Potential and Temperatu
r
e Dis
t
r
i
bution alon
g Inside the
Wa
ter Bubbl
es
The ele
c
tri
c
field distri
buti
on, potential and tempe
r
at
ure in
side th
e water b
u
b
b
le are
highe
r
initially
and
then de
cre
a
ses with small cha
nge
becau
se the
distan
ce va
ri
ation is in mi
cro
meters. Here
for different case
s
numb
e
rs of
wate
r b
u
bble
s
a
r
e va
ri
ed d
epen
ds o
n
water
bub
bl
e
radiu
s
thu
s
e
l
ectri
c
field,
potential an
d
temper
ature
is cal
c
ul
ated
inside th
e b
ubble. Th
us t
he
cha
nge in Pot
ential, field and Temp
erat
ure is
sho
w
n i
n
Figure 10.a
,
10.b and 11.
a, 11.b.
Potential (V)
Figure 10.a. Electri
c
Potential Distri
buti
on
along In
side t
he Wate
r Bub
b
les 1
1
kV
Figure 10.b. Electri
c
Potential Distri
buti
on
along In
side t
he Wate
r Bub
b
les 2
0
kV
2.2
2.4
2.
6
2.
8
3
3.2
3
04.3708
304.371
3
04.3712
3
04.3714
3
04.3716
3
04.3718
H
o
r
i
z
o
nta
l
di
s
t
a
n
c
e
(
m
m)
T
e
m
p
er
at
u
r
e(
K
)
4.
649
4.
65
4.
651
4.
652
4.6
5
3
4.
65
4
30
5.5
4
8
30
5.5
4
9
30
5.
55
30
5.5
5
1
30
5.5
5
2
30
5.5
5
3
Ho
r
i
zo
n
t
a
l
d
i
s
t
a
n
ce(
m
m
)
T
e
m
p
er
at
ur
e
(
K
)
2.822
2.823
2.824
2.825
2.826
2.827
9986
9988
9990
9992
9994
9996
9998
P
o
te
n
tia
l(V
)
H
o
ri
z
o
nta
l
di
s
t
a
n
c
e
(
m
m
)
4.
6
495
4.
65
4
.
650
5
4.
651
4.
6
5
15
4.
65
2
4.
6525
4.
653
4.
6535
4.
654
886
0
887
0
888
0
889
0
890
0
891
0
Ho
r
i
z
o
nt
a
l
dis
t
a
n
c
e
(
mm
)
P
o
t
e
n
t
ia
l(
V
)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 595
4 –
5962
5960
Field (kV/m)
Figure 11.a. Electri
c
Field
Distri
bution al
ong
Inside the
Wa
ter Bubble
s
1
1
kV
Figure 11.b. Electri
c
Field
Distri
bution al
ong
Inside Water Bubble
s
20
kV
The tempe
r
at
ure di
stributio
n along wate
r bubbl
e is illustrate
s in Fi
gure 1
2
.a an
d 12.b.
The tempe
r
a
t
ure at the condu
ctor
surf
ace to the first wate
r bu
bble is mo
re
compa
r
e wi
th
temperature along water
b
ubble curve
i.
e.
variati
ons i
n
temperature is very less. The maximum
boun
dary
con
d
ition of tem
peratu
r
e
at condu
ctor
su
rf
ace i
s
3
63K
and o
u
ter
sh
eath tempe
r
a
t
ure
is 293K so the temperature is in
the ran
ge of 328K in
this ca
se.
Tempera
t
ure
(K)
Figure 12.a. Tempe
r
atu
r
e
Distri
bution al
ong
Inside the
Wa
ter Bubble
s
1
1
kV
Figure 12.b. Tempe
r
atu
r
e
Distri
bution al
ong
Inside the
Wa
ter Bubble
s
2
0
kV
3.4. Electric
Field, Pote
ntial an
d T
e
mperat
u
r
e
Distribution
a
l
ong th
e
Ra
dial Line
Water
Bubble
s
The re
gion
s l
o
cate
d in the
vicinity of th
e sha
r
p e
dge
s of the wate
r parti
cle
s
, especi
a
lly
those
clo
s
e to the cond
uctor su
rface and cha
r
a
c
te
ri
zed by a hig
h
field are su
itable points
fo
r
tree initiation.
The growth
of such trees means
a hi
gh field will be originated at
the tip of the
stru
ctural
cha
nnel
s of the
s
e tree
s,
whi
c
h can in
evitably affect tho
s
e l
o
w fiel
d a
r
ea
s
with tim
e
. If
the water absorption process co
ntinues, the number of water
particles will
increase and
con
s
e
que
ntly the numbe
r
of high-fiel
d region
s al
so
i
n
crea
se
s. Th
e elect
r
ic fiel
d distri
bution
from
con
d
u
c
tor surface is hig
her compa
r
e wit
h
electri
c
field
along the tip of the water b
ubble. He
re f
o
r
different ca
se
s numb
e
r of water b
ubbl
e
s
is varie
d
de
pend
s on water bub
ble Ra
dius thu
s
ele
c
tric
field is
cal
c
u
l
ated e
a
ch
e
nd p
o
int of
every bu
bbl
e
i.e. tip of the
water bu
bble. Initially a
t
con
d
u
c
tor su
rface
i
s
hi
gh
er fo
r eve
r
y
water b
ubble
field di
stri
but
es
with
grad
ual
cha
nge.
Thus
the cha
nge in
field and pot
ential is sho
w
n in Figure 13
, 14, 15, 16 and 17.
2.
822
2.8
2
3
2.
824
2.8
2
5
2.8
2
6
2.
827
2.
6
2.
7
2.
8
2.
9
3
x 1
0
6
H
o
r
i
zo
n
t
a
l
d
i
s
t
a
n
ce(
m
m
)
E
l
ect
r
i
c F
i
el
d
(
V
/
m
)
4.
649
4.
6495
4.
65
4.
6505
4.
651
4.
6515
4.
652
4.
6525
4.
653
4.
6535
4.
654
7.
6502
7.
6503
7.
6504
7.
6505
7.
6506
7.
6507
7.
6508
7.
6509
x 10
7
Ho
riz
o
n
t
al
d
i
s
t
a
n
ce(
m
m
)
E
l
ect
ri
c f
i
el
d
(
V
/
m
)
2
3
4
5
6
7
303.
4
303.
6
303.
8
304
304.
2
304.
4
Ho
r
i
zo
n
t
a
l
d
i
s
t
a
n
ce(
m
m
)
T
e
m
p
er
at
u
r
e(
K
)
4.6
4
9
4.6
495
4.65
4.650
5
4.6
5
1
4.
6515
4
.
652
4
.
6525
4.65
3
4.6
535
4.6
5
4
3
05.54
7
3
05.54
8
3
05.54
9
305.5
5
3
05.55
1
3
05.55
2
H
o
r
i
z
o
nta
l
di
s
t
anc
e
(mm
)
Te
m
p
e
r
a
t
u
r
e
(
K
)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Electri
c
Field
and The
r
m
a
l Prope
rties of
Wet Ca
ble: Using FEM (S
u
s
hm
an Kum
a
r Kanikella)
5961
Potential (V):
Figure 13. Electri
c
Potenti
a
l Distri
bution
along
the Radi
al Lin
e
Con
n
e
c
ting
Numbe
r
of Wate
r
Bubble
s
11
kV
Figure 14. Electri
c
Potenti
a
l Distri
bution
along
the Radi
al Lin
e
Con
n
e
c
ting
Numbe
r
of Wate
r
Bubble
s
20
kV
Field (kV/m)
Figure 15. Electri
c
Field
Di
stributio
n alo
ng
the Radi
al Lin
e
Con
n
e
c
ting
Numbe
r
of Wate
r
Bubble
s
11
kV
Figure 16. Electri
c
Field
Di
stributio
n alo
ng
the Radi
al Lin
e
Con
n
e
c
ting
Numbe
r
of Wate
r
Bubble
s
20 kV
Tempera
t
ure
(K)
Figure 17. Te
mperature
Di
stributio
n alo
ng
the Radi
al Lin
e
Con
n
e
c
ting
Numbe
r
of Wate
r
Bubble
s
11
kV
Figure 18. Te
mperature
Di
stributio
n alo
ng
the Radi
al Lin
e
Con
n
e
c
ting
Numbe
r
of Wate
r
Bubble
s
20
kV
3
3.5
4
4.
5
5
5.
5
6
0
2000
4000
6000
8000
1000
0
H
o
rin
z
o
n
ta
l dis
t
a
n
c
e
(
m
m
)
P
o
t
e
n
t
ia
l(
V
/
m
)
3
4
5
6
7
8
9
10
0
0.5
1
1.5
2
x 10
4
H
o
r
i
z
o
n
t
al
d
i
s
t
an
c
e
(
mm
)
P
o
t
e
n
t
ia
l(
V
)
3
3.5
4
4.5
5
5.5
6
2.6
2.8
3
3.2
3.4
x 1
0
6
H
o
ri
z
o
nt
a
l
dis
t
a
n
c
e
(
m
m
)
E
l
ect
r
i
c F
i
el
d
(
V
/
m
)
3
4
5
6
7
8
9
10
2.5
3
3.5
4
4.5
x 10
7
Ho
r
i
z
o
nt
a
l
dis
t
a
n
c
e
(
mm
)
E
l
ec
t
r
i
c
f
i
el
d
(
V
/
m
)
2
3
4
5
6
7
303
.4
303
.6
303
.8
304
304
.2
304
.4
Ho
r
i
zo
n
t
a
l
d
i
s
t
a
n
ce(
m
m
)
T
e
m
p
er
a
t
u
r
e(
K
)
3
4
5
6
7
8
9
10
300
310
320
330
340
350
360
370
H
o
ri
z
o
n
t
al
di
s
t
an
ce(
m
m
)
T
e
m
p
er
a
t
u
r
e(
K
)
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 595
4 –
5962
5962
The
temp
erature distri
butio
n
from co
ndu
ctor su
rfa
c
e t
o
the
radial
li
ne conn
ectin
g
wate
r
bubbl
e is illustrated in Figu
re 17 an
d 18.
The tempera
t
ure at the vicinity of the water pa
rticle
s
is
greatly inten
s
ified com
pare
d
with
that at
the sam
e
lo
cation wh
en th
e wate
r pa
rticles a
r
e a
b
sen
t.
The maximu
m bound
ary con
d
ition of temperatur
e
at condu
cto
r
surfa
c
e is
363K and o
u
ter
s
h
eath temperature is
293K.
4. Conclusio
n
In this pape
r a study of electri
c
field, el
ectri
c
potenti
a
l and tempe
r
ature distri
b
u
tion in
wet
cable
in
sulation fo
r 11
kV an
d 2
0
kV
power
cable
are
en
deav
ored
u
s
ing t
w
o-dime
nsio
nal
finite eleme
n
t ba
sed
mo
de
ls of
the
po
wer
ca
ble
s
. Th
ese
mo
dels
were
used to
co
mpute
the
electri
c
field
and te
mpe
r
at
ure
di
stributio
n in
side
the
i
n
sul
a
tion
and
the field
e
n
h
ancement
at
the
tips of elli
ptical wate
r p
a
rti
c
le
s. Accordi
ng to t
he
re
sults, we
can
see th
at
the t
e
mpe
r
ature i
n
the
con
d
u
c
tor
co
re of
cabl
e i
s
mo
re. Thi
s
is du
e to t
he po
we
r lo
sses i
n
the
con
d
u
c
tor. T
he
temperature
decrea
s
e
s
when we com
e
to the outer
she
a
th of the ca
ble. It is sh
owed tha
t
the
highe
st di
stri
bution i
n
the
co
ndu
cto
r
while the
cabl
e in
sulatio
n
near g
r
ou
nde
d sho
w
ed
lo
we
r
distrib
u
tion of
tempe
r
atu
r
e as acco
rdin
g to
giv
en bou
n
dary co
nditio
n
.
It
wa
s ascertaine
d
that
the
field enha
ncement is
strongly
su
bord
i
nated up
on
the sha
pe a
nd ab
so
rbed
water p
a
rticles.
Eventually, the rol
e
of el
ectri
c
field in
the
power
cable an
d the
possible
me
cha
n
ism
s
of
the
insul
a
tion agi
ng and b
r
ea
k
down due to
water infe
stat
ions a
r
e b
r
iefl
y addre
s
sed.
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